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On the Behaviour of a Series Associated with the Conjugate Series of a Fourier Series

Published online by Cambridge University Press:  20 November 2018

R. Mohanty  and
B. K. Ray
R. Mohanty
Affiliation:
Ravenshaw College, Cuttack (Orissa), India
B. K. Ray
Affiliation:
Ravenshaw College, Cuttack (Orissa), India
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1.1. Definition. Let λ ≡ λ(ω) be continuous, differentiable, and monotonic increasing in (0, ∞) and let it tend to infinity as ω → ∞. Suppose that ∑ an (we write ∑ for throughout the present paper) is a given infinite series and let

The series ∑ an is said to be summable |R, λ, r|, where r > 0, if

where A is a fixed positive number (6, Definition B). Now, for r > 0, m < ω < m + 1,

Hence, ∑ an is summable |R, λ, r|, where r > 0, if

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 535 - 551
Copyright
Copyright © Canadian Mathematical Society 1969

References

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